Fixed - well it wasn't actually broken! As I suspected, a button had got pressed. If you hold down one of the buttons for ten seconds, and then press a different button, the oven gets put in "demo mode." This means that it won't turn on the heating elements or the fan whatever you turn the knob to. The lights come on, and the buttons adjust the temperature, but nothing happens. And it remembers it has been put into this mode even if you turn it off and on again at the wall!

So fortunately it wasn't really broken, and I should have read the small print in the manual more carefully!